Typically, blurring is used as an artistic effect to remove unwanted detail or to make something appear to be in motion. We are going to use blurring to remove some of the artifact from the texture of the paper.
Take a look at the original (left) and the blurred (right) photo:
I used the Blur command in Picture Window. Specifically, I used a gaussian blur, which averages pixels in a specified radius such that closer pixels have a greater impact. I used a small radius for blurring, only 2 pixels, and set it for 75% of maximum effect. You can set a threshold for gaussian blur, such that if the difference between the pixel in the original and the pixel in the blurred image is greater than the threshold, the image is not blurred. This selectively blurs already soft parts of the image. This way you can, for example, reduce graininess in the sky but not affect a tree line in the image (Picture Window's example). Here I did not use a threshold (left it a maximum - 255) since unfortunately some of the sharpest areas of contrast from one pixel to the next are in the texturing of the paper.
This technique took a bit to figure out, but if you are in a position that you need to get rid of background texture, it is worth experimenting with the blur command. I've found that a gaussian blur with a radius in the 2-3 pixel range works pretty well. With this image, I played with the amount of blurring until I got the image I liked best (turned out to be 75% full effect). This task is similar to the Unsharp Mask from case 1 - you experiment until you get the optimal balance between avoiding graininess while maintaining sharp features on the photo subject.
A potential alternative to blurring would be to place the image on a copy stand instead of a scanner, and if the light is flat enough, then some of the texture might not show in the image made of the photograph. Case 3 shows a comparison of capturing an image using the scanner versus using a copy stand.
Now that the photo doesn't look quite so much like it was printed on sandpaper, it is time to work on color correction.